Vectors in the Plane

$\rhd$ Introduction to vectors and scalars (8:38) A discussion on vectors and scalars.
Recognizing vectors (2:35) Which of the following can represent a vector? Select all that apply.
1. The number 5
2. The angle measure $5^{\circ}$
3. The point $(5,5)$
4. The outcome of $5+5$
* Practice: Recognizing vectors. (2 problems)
$\rhd$ Equivalent vectors (6:36) When are two vectors equivalent.
* Practice: Equivalent vectors. (4 problems)
$\rhd$ Finding the magnitude (3:05) The magnitude of $\vec{a}= \langle 5,-3\rangle$ .
$\rhd$ Scalar multiplication of vectors (5:41) Given that $\vec{w}= \langle 1,2\rangle$ , find $3\vec{w}$ and $-2\vec{w}$ . What do they represent geometrically?
* Practice: Scalar multiplication. (4 problems)
$\rhd$ Adding and subtracting vectors (7:41) Given that $\vec{a}= \langle 3,-1\rangle$ and $\vec{b}= \langle 2,3\rangle$ , what are $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$ ? What do they represent geometrically?
$\rhd$ Combined vector operations (5:58) Given that $\vec{u}= \langle 2,-1\rangle$ and $\vec{w}= \langle -5,5\rangle$ , what are $3\vec{u}+\dfrac{1}{5}\vec{w}$ and $\vec{a}-\vec{b}$ ? What does it represent geometrically?
* Practice: Combined vector operations. (4 problems)
$\rhd$ Finding unit vector with given direction (5:01) Find a unit vector in the direction of $\vec{a}= \langle 3,4\rangle$ .
* Practice: Unit vectors. (4 problems)
$\rhd$ Direction of a vector (1st and 2nd quadrant) (9:00) Find the directions of $\vec{u}= \langle 3,4\rangle$ and $\vec{w}= \langle -5,6\rangle$ .
$\rhd$ Direction of a vector (3rd and 4th quadrant) (6:41) Find the directions of $\vec{a}= \langle -2,-4\rangle$ and $\vec{b}= \langle 4,-6\rangle$ .
* Practice: Direction of vectors. (4 problems)

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The OpenLab at City Tech:A place to learn, work, and share

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